Anecdatum, but I play competitive basketball on a very low carbohydrate diet (<20g/day), and feel just fine, so necessary seems necessarily false.

The missing concept (in the brief quote in your comment) might be "fat adaptation", which takes (in my experience) 2-4 weeks (details: http://www.artandscienceoflowcarb.com/the-art-and-science-of... )

One certainly can fuel activity with carbohydrates, but a fat-adapted person should have no trouble with physical activity on a (very) low carbohydrate diet. Interestingly, a fat-adapted athlete can still use carbohydrates for supplemental fuel before, during, or immediately following extreme exertion (no adaptation is required for short-term use of carbohydrates).